Exercises: Understand Graphs of Equations

Show all substitution work when verifying points. For graphing problems, generate a table of values before plotting.

Grade 9·23 problems·~30 min·Common Core Math - HS Algebra·standard·hsa-rei-d-10

Work through problems with immediate feedback

Fluency Practice

Determine whether each given point lies on the graph of the equation. Show your substitution.

Is the point $(3, 4)$ on the graph of $x^2 + y^2 = 25$ ?

Yes — $3^2 + 4^2 = 9 + 16 = 25$ ✓

No — circles don't pass through points with equal $x$ and $y$ values.

Yes — $3 + 4 = 7$ and $25 \div 7 \approx 3.6$ , which is close.

No — $3^2 + 4^2 = 12 + 16 = 28 \neq 25$ .